I like the concept behind the rule. The notion that some items can be more powerful than items of equivalent rarity but with the balancing factor that you can only draw that extra power out of a certain number of them is a decent idea. However, I also know that groups often run very different games and either the three item limit or the requirement of attunement for certain specific items may not seem the right for some groups.
Ultimately, what I think of the most when it comes to attunement is an intelligent magic item that I gave to a PC in a campaign a few years ago. The item was very vain and jealous, and it refused to work if its bearer was also wearing/using other magic items.
I use the following depending on if I am DMing a high magic or standard magic game. For high magic I use the proficiency bonus as the number of items that can be attuned. I find this to be a good balance as the heroes progress through the different tiers.
For most normal games I just use the default attunement rules of three.
The system is great and the number is great. Just some itens could change.
But if you like ultra item power (10 rings, 5 amulets, 3 belts...) just ignore it.
I was thinking in a BBGE in the future that is a magic item collector, with some power that ignore attunement and lots of magic itens hunting the PCs for they tresure.
I think I saw that on a cartoon, don't remember the name...
I like the concept of attunement in that attuning to a magical sword unlocks its greater magical powers, but part of me doesn't like it or doesn't like the limit of 3. Really though, I think we need to see some higher level play with more items before I can have a proper opinion on it.
I agree - I like the attunement as a kind of binding the PC to the item, and that process enables the item to grow in power/unlock/awaken other abilities of the item over time. I really like that scaling ability of the item which I think attunement fits well with (or indeed, turning a non-magical sword into a magical one, like an heirloom item or something?). I think that works really well with "low magic" worlds - the PCs still get various interesting magic item abilities, but fewer individual items, as such.
Part of what I like about attunement is personalizing the attunement process. For example, in a recent running of the LMoP adventure the PCs found a necromantic magic item. In order for a PC to attune to the item, he had to feed the magic item his own blood.